{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 1,
     "metadata": {
      "image/png": {
       "width": 200
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image('../../Python_probability_statistics_machine_learning_2E.png',width=200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- TODO: sklearn.random_projection, sklearn.manifold -->\n",
    "<!-- TODO: subspace optimization discussion -->\n",
    "\n",
    "\n",
    "The features from a particular dataset that will ultimately prove important for\n",
    "machine learning can be difficult to know ahead of time.  This is especially\n",
    "true for problems that do not have a strong physical underpinning. The\n",
    "row-dimension of the input matrix ($X$) for fitting data in Scikit-learn is the\n",
    "number of samples and the column dimension is the number of features. There may\n",
    "be a large number of column dimensions in this matrix, and the purpose of\n",
    "dimensionality reduction is to somehow reduce these to only those columns that\n",
    "are important for the machine learning task.\n",
    "\n",
    "Fortunately, Scikit-learn provides some powerful tools to help uncover the most\n",
    "relevant features.  Principal Component Analysis (PCA) consists of taking\n",
    "the input $X$ matrix and (1) subtracting the mean, (2) computing the covariance\n",
    "matrix, and (3) computing the eigenvalue decomposition of the covariance\n",
    "matrix. For example, if $X$ has more columns than is practicable for a\n",
    "particular learning method, then PCA can reduce the number of columns to a more\n",
    "manageable number.  PCA is widely used in statistics and other areas beyond\n",
    "machine learning, so it is worth examining what it does in some detail. First,\n",
    "we need the decomposition module from Scikit-learn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import decomposition\n",
    "import numpy as np\n",
    "pca = decomposition.PCA()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's create some very simple data and apply PCA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.00000000e+00 2.73605815e-32 8.35833807e-34]\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace(-1,1,30)\n",
    "X = np.c_[x,x+1,x+2] # stack as columns\n",
    "pca.fit(X)\n",
    "print(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Programming Tip.**\n",
    "\n",
    "The `np.c_` is a shorcut method for creating stacked column-wise arrays.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    " In this example, the columns are just constant offsets of the first\n",
    "column. The *explained variance ratio* is the percentage of the variance\n",
    "attributable to the transformed columns of `X`. You can think of this as the\n",
    "information that is relatively concentrated in each column of the transformed\n",
    "matrix `X`. [Figure](#fig:pca_001) shows the graph of this dominant\n",
    "transformed column in the bottom panel.  Note that a constant offset in each of\n",
    "the columns does not change its respective variance and thus, as far as PCA  is\n",
    "concerned, the three columns are identical from an information standpoint."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from matplotlib.pylab import subplots\n",
    "fig,axs = subplots(2,1,sharex=True,sharey=True)\n",
    "ax = axs[0]\n",
    "_=ax.plot(x,X[:,0],'-k',lw=3)\n",
    "_=ax.plot(x,X[:,1],'--k',lw=3)\n",
    "_=ax.plot(x,X[:,2],':k',lw=3)\n",
    "ax=axs[1]\n",
    "_=ax.plot(x,pca.fit_transform(X)[:,0],'-k',lw=3)\n",
    "#ax.tick_params(labelsize='x-large')\n",
    "fig.savefig('fig-machine_learning/pca_001.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/pca_001.png, width=500 frac=0.75]  The top panel shows the columns of the feature matrix and the bottom panel shows the dominant component that PCA has extracted.  <div id=\"fig:pca_001\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_001\"></div>\n",
    "\n",
    "<p>The top panel shows the columns of the feature matrix and the bottom panel shows the dominant component that PCA has extracted.</p>\n",
    "<img src=\"fig-machine_learning/pca_001.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "To make this more interesting, let's change the slope of each of the columns as\n",
    "in the following,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.00000000e+00 3.26962032e-33 3.78960782e-34 2.55413064e-35]\n"
     ]
    }
   ],
   "source": [
    "X = np.c_[x,2*x+1,3*x+2,x] # change slopes of columns\n",
    "pca.fit(X)\n",
    "print(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " However, changing the slope did not impact the explained variance\n",
    "ratio. Again, there is still only one dominant column. This means that PCA is\n",
    "invariant to both constant offsets and scale changes. This works for functions\n",
    "as well as simple lines,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.00000000e+00 3.70493694e-32 2.51542007e-33]\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace(-1,1,30)\n",
    "X = np.c_[np.sin(2*np.pi*x),\n",
    "          2*np.sin(2*np.pi*x)+1,\n",
    "          3*np.sin(2*np.pi*x)+2] \n",
    "pca.fit(X)\n",
    "print(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Once again, there is only one dominant column, which is shown in the\n",
    "bottom panel of [Figure](#fig:pca_002). The top panel shows the individual\n",
    "columns of the feature matrix. To sum up, PCA is able to identify and eliminate\n",
    "features that are merely linear transformations of existing features. This also\n",
    "works when there is additive noise in the features, although more samples are\n",
    "needed to separate the uncorrelated noise from between features.\n",
    "\n",
    "<!-- dom:FIGURE: [fig-machine_learning/pca_002.png, width=500 frac=0.85] The top panel shows the columns of the feature matrix and the bottom panel shows the dominant component that PCA has computed. <div id=\"fig:pca_002\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_002\"></div>\n",
    "\n",
    "<p>The top panel shows the columns of the feature matrix and the bottom panel shows the dominant component that PCA has computed.</p>\n",
    "<img src=\"fig-machine_learning/pca_002.png\" width=500>\n",
    "\n",
    "<!-- end figure -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs = subplots(2,1,sharex=True,sharey=True)\n",
    "ax = axs[0]\n",
    "_=ax.plot(x,X[:,0],'-k')\n",
    "_=ax.plot(x,X[:,1],'--k')\n",
    "_=ax.plot(x,X[:,2],':k')\n",
    "ax=axs[1]\n",
    "_=ax.axis(xmin=-1,xmax=1)\n",
    "_=ax.plot(x,pca.fit_transform(X)[:,0],'-k')\n",
    "# ax.tick_params(labelsize='x-large')\n",
    "fig.savefig('fig-machine_learning/pca_002.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GBweBphxEoVC4YedgMNxumBWAYde5WjVPpf0TCoUYGxvD7XYjhKBarTI+Pk4wGARMSqjBcL2YFYBh12kv7gL074WFhXVXASoV1OfzEQqFCIVCuN1uZmdnuXjxIuFwmHA4bOQgDIbrxBgAw66SzWY5d+4c1WqVWq2G1+slGo0Sj8d1vv9aRkdHmZ6eBppunkwmQzKZZGJignq9TrFYpFQqcd9995ksIIPhOjAGwLBrZLNZnn32WVZWVsjlcni9XrxeL263m1wux549e9Z9XHsqaKFQIJ/PMzExQTwe18fYtk0+n79Rp2Iw3JYYA2DYNc6ePUsqlUIIgdvtBqBcLpPNZolEIquOXS9IfNdddwHw1FNPUSgUWFhY0KuISCSiXUkGg+HaMAbAsGssLi4SCAQolUpEo1Fs26bRaFAsFnnZy16GkoBSQWK/348QgosXL3Lq1Cn27dvH0NAQ6XSaYrFIJpPRqaC2bRMKhchms8YNZDBcI8YAGHYNNcFblkW9XicajeI4Do7jYFkWlmUBLwWJHcdhYWEBr9dLOBxmbm6OkydPIqVkZWVF5/7XajWSySTDw8MbBpINBsPWmDRQw66hdH3U5G7bNrZtE41GqVQqWtRNpX2mUim8Xq82GKlUikajQa1Ww+12UyqVyGazOI6D1+vFcRzTFtJguA7MCsCwaxw4cIBCoUC5XCYYDGLbNl6vl/HxcQ4cOEAsFtMtH+fm5nTjF8uyyOVyetJPJpNIKZFS4vF4EELgcrlIp9OMjY11+jQNhlsWYwAMu0YsFuPo0aMbVgAr338kEqFSqSClZHl5md7eXtLpNLVajVKpRL1e189Zq9X0qsCyLCMNbTBcB8YAGHaVWCy2asJfWFjgzJkzhEIhSqWSLhDzer0IIVhaWmJpaUnn+q9Ho9Gg0WisMgwGg+HqMTEAww1hPTmImZkZHMcB0KuDnp4eUqnUhpO/QmUDGTE4g+HaMSsAww2hPdNneXkZ27apVqvMzs5y5513kkgkOH/+PPl8nq06hAohkFJi2zbJZPIGnYHBcPthDIDhhlAsFvUdu9fr1cZgaWmJaDTK7OwsUkocx9nSAMBLekKqV7DBYLh6jAvIsOuoTJ/nn3+efD5Po9FACIHf72doaIjLly9Tq9V0PEDVB2yEEAKPx4Pb7cbv99+gszAYbj9uRE/gPxVCLAshTrZt6xVCfFEIcab1O77ZcxhufrLZLKdPn+bEiROcPn1aSz23Z/qowG0ymdQaPx6Ph3w+TygUol6vk8/nt8ztl1JSLBYJh8P09/ffiNMzGG5LboQL6KM0m8D/edu2XwK+LKX8TSHEL7X+/8UbMBbDLtAu5RAOh8lkMpw5c4ZAIEAymcTj8dDb20s8HqdcLuM4DtlslmAwiJSSaDRKtVplcXERKSVut3vTDB8VAK5Wq1doChkMhu2z6ysAKeWTQGrN5keAP2v9/WfAG3d7HIbdo13vv1QqkUgkqNVqLC4uUqlUKJfLFItF6vU6Pp+PwcFBarUa5XKZRCKBz+fTaqHVanXDyV+5ftTveDxuFEENhuugU0HgISnlIoCUclEIMdihcRh2AOWOAbScg0rjDIVCFItFFhYWkFJqI6AUQV0uF4uLi6TTaV3tuxEulwufz0ej0cDn8xGPx40UhMFwHdz0QWAhxHuEECeEECcSiUSnh2NYB9XBC5o6/R6PB9u2dUA3l8tRKBRwuZqXm+rt63K5sG2bUqlEo9HYVvYPgNvtxufzEQ6Hb+mWkObaNnSaThmAJSHECEDr9/JGB0opH5VSHpNSHhsYGLhhAzRsHyX6pib9crkMQCAQoFarIYQAmisFKaW+ky8Wi9i2ve2KXsuydIxg7969uFyuW1oKwlzbhk7TKQPwaeAnW3//JPB4h8Zh2AFUB69arUYmk2F5eVlP/isrK6vcNC6Xi3K5TKVSodFoUKlUNszld7vdeDxNL6XqJjY8PMyRI0eYnJzk8OHDRgraYLgOdj0GIIT4K+AhoF8IMQf8MvCbwMeFED8NXAL+6W6Pw7CzrO3gFYlEqNfrHDp0iFqtRiKRYGlpiVKppCfxWq2mxdxs2wbQUhDr0Wg0sCyLaDTKyMgIqVSKYrHIzMwMtm0TiUSMATAYroNdNwBSyrdusOvh3X5tw+6wNu2zWq3yrW99i8HBQXw+n/bPQ3OCV9r+LpcLKeVVCblFIhGi0ajWBwqFQtRqNebn58lmszz44IOMj4/v5ukaDLctN30Q2HDz0Z72KYTA5/MhpaRQKKw6znEchBBa3kGleHo8Hh0Q3gwpJel0moWFBVZWVqjX6/r1lDE5ffr0bp2mwXDbY7SADFdNe9qnIhQKkUo1yz1U1k8qldL+/fbG8G63WxuHrTJ/2t1FKtCs4gEej4dcLrfTp2cwdA3GABiuGpX2qQTZoDmp5/N53G43mUyGUqlEpVLRKwCl4a+KuFwu1zXr+auU01wuh8meMRiuHeMCMlw17WmfSpY5n88zNjZGKpUinU7TaDS0YJvL5aLRaOjHr+3ytR4bCcKpYjG1cujp6dm5EzMYugyzAjBsm/bMH7fbTa1Wo1qtIoSgXC6TTCZxHIdgMIhlWaysrFCtVle5edrdPmsNQzu1Wm3TsViWxeDgoFEDNRiuA7MCMGyLtR29LMuiXq8zPDxMvV6nXq9rv7xt29i2vaq6tz0GAOiJ37KsVfn+qmhsI4QQhEIhotEo8Xj8lq4ENhg6jVkBGLZFe+ZPsVjUOfnnzp1j3759+P1+isWi9u2v7eyl3Dbtd/xSyivu9IUQCCE2XBlIKSmVSni9XgKBwC1dCWwwdBqzAjBsi2KxiNfrpVgsMj8/T71e143dZ2dnKZVKlEolPfGvl92zdtt6x6hg8WaoFND9+/ebQjCD4TowKwDDuqyt9FX6+0rt07IsarUaXq+XdDpNuVzWwd1Go6HdOo1GQ9/lb1fsbSMsy8LlchEOh/H7/UYK2mC4TowBMFxBe6WvEIKLFy+SSqW0FHM8HqdWq5HP56lUKqTTaV2kpVxAqtp3s7v57dQBtKPaRqq/TUN4g+H6MC4gwxUof7/jOCwsLCCEoLe3F4/HQ6lUIp1Or6ryVU1a2o2A0v7fzAAoZc/t4nK58Hq9uFwu/H4/mUxGt540GAxXjzEAhitQ/n7l7qnX62SzWVKpFMFgkHw+TyKRwLZtLfNgWRYej0cXfcGVLp/15B+uthis0Wjg9XqJRqMMDAywsLBw7SdqMHQ5xgXUhaz174+Ojq4KpqpKXyXBkE6nAfB4PBSLRV0FrLT+LcvCtu1Ns3c2y/nfLmpV0dfXx969ewkEAlfoDxkMhu1jVgBdxtp8/lqtxvT09CpXiqr0dbvdZLNZarUahUJB+/xVoZdlWQQCAZ31o4K9yg2kqoADgYAO4LazVc7/evh8Pl0zUK1WTR2AwXAdmBVAl9Gezw/o38qV0l7pGw6HOX/+PNCUZS4UCrrIy3EcLMtCCKG7erW7fFwulw7yOo6j/3e73Xr71a4IlOxEo9FgaWmJ3t5eJicnd+JtMRi6EmMAuoz1lDy9Xi+JRIJ8Pr9K419V+pZKJV2gpSQgVDcv27axLItQKKR7/arqXqUVJKXUNQNKyO1qaF8pNBoNUqkU/f39piOYwXCdGAPQZayn5FmtVqlUKsRisStWBlJKotGo1vxfWVmhXC5rXX+Px0MgEMDn8+nm7tVqdZW7R2X6bNb9azOklAghCAaD+P1+XC4XBw4cMJO/wXCdGAPQZYyOjjI9PQ2gWzeqO/e+vj4cxyGVSmlN/0wmoyfeQqGA2+3G7XavEnRTE7RaIbR3/nK5XDoA7PV6N+z/q/D7/VpbSLmIVBxBFaQ5jmMkIAyGHcAYgC5DNXA/e/YsMzMzhMNh7rjjDpaXlzlz5oyu3r18+bKerNXdfbFY1BLPbreber2u+/yquIDL5SIUClGv13XjdymlThHdCsdxdKWxyvoZGhrCcRxs2yYQCBjXj8GwQ3TUAAgh/g3wLkACzwPvlFJufotouG5isRjBYJBDhw5pV8/g4CCXL1/WgVZV4OXz+ahUKrhcLj3BBwIByuUy1WpVyz643e5V/v32jKB6vb7tdE3lWhoaGsKyLBYWFnC5XASDQQYHB4nH49xzzz07/6YYDF1IxwyAEGIM+DngZVLKshDi48CPAR/t1Ji6ibXB4FAoRCQSYXl5mXq9rqttlbyzSuW0LEsbBVX8Va1Wr5j8lUHYSBhuMxqNBuFwmHq9zv33309fX9+GNQsGg+Ha6bQLyAMEhBA1IAiYss4bQDabJZ1OMzc3RyQSobe3l2AwqH37Ho9Hp3VKKfXdfzgcRgjBwMAApVKJVCqlJ3tlFGzb1po9yk20XQPQHjhWcs/33HOPmfANhl2iYwZASjkvhPht4BJQBr4gpfxCp8bTDWSzWe37Vw1dMpkMc3NzSCnJZDI6WAtQKBR04VWlUtHaPefPn6dSqWhhNsdxKJfLwEsVv1sFe9cSCARoNBq6RmFyctLc7RsMu0zHKoGFEHHgEWAfMAqEhBBvW+e49wghTgghTiQSiRs9zNsGVQGcSCS0nLJt2+RyOWzbJp1OE4lECIfD+s5f9eVVej9+v594PK6Ds9FoVLt/VDD4WuQeVOaQ3+8nEolw4MAB7rrrrtt+8jfXtqHTdNIF9P3AjJQyASCE+Fvg+4C/aD9ISvko8CjAsWPHrk9QvotRFcD1el3LPAsh8Pl8BINBqtUqkUiERqOB4zjafaN093O5nHYdKSXQ5eXlVZO+koDYjhFol45WtQmAlnmYm5sjn8/f1r5/c20bOk0nDcAl4HuFEEGaLqCHgRMdHM9tjQr6+nw+HMfRCp9qsld+f5WxEw6HKZfLuN1ucrkcHo9HN4Fvjw+0V+muF/BVfv12I6GCyapgrFar4XK5sCyLdDqNx+NheXmZ/fv309PTQ7VaZXp62qR/Ggw7TMdcQFLKbwKfAL5FMwXURetuyLDzqLvs3t5eLecMzTtupdeTSCS4fPmyDuRWq1UKhQIul0urgKq8fjXRbxXgXdviUU30qrF8IBDAcRwdR/B4PNotlUql9CrF7/cb6WeDYYfpqBqolPKXpZR3SinvllK+XUppd3I8tzNK4dPj8egMHZfLhc/nIxaLUavVKJVK2pefy+UIBoMUi0U9IddqtWtK62xHSUWoVYXP51tV6dtoNLQYXSqV0o9T/YgNBsPO0ek0UMMNQlUALywsYNs2w8PDBAIB0uk0Fy5c0JN7NBrF6/XSaDTI5XI6u0exE5r+ygg0Gg2t7qncSfV6Ha/XS7lcJhQKUSwWSaVSFItFgsEg2WzWuIEMhh3CGIAuIhaL6ckzm82SSCS0+0dJNJdKJd3VS0k5qAn6elGBZxX8VY3lAR0EbjQaeDwestksHo+HmZkZfD4fQggikYiJBRgMO4gxAF1IJBJhamqKQqFAtVqlWCzq6t/2Kl6l+b8TBkAZGCUYpySki8Wilp9Q210uF/F4HI/HQzqdZnR0lLGxMYLBILZts7CwYAyAwbADmI5gXYZqB6n0+lVPXnVn3p7GqaqAVeBWpWi2s92uXu3qoS6XS+sRqbt7j8dDOBzWyqODg4NIKQkGgwD6t4kFGAw7h1kBdBlnz54llUqRz+eRUhIIBPTdfrt/v6enh2w2q+/YVTGYupNXbHdloLJ5lDHxer04jkMgEMDr9eq7e2hO9oFAQAeel5aWGBkZ0fUKpg2kwbAzGAPQRWSzWS0B7fP5KBQKpNPpVZO4auyuXDPKMLRr86tVw3ZQE//Q0JAWlYOmrz+fz2v1z4GBAXp7e1lZWaHRaGBZFpFIhEQigWVZrKys4Ha7qVQqpg2kwbBDGAPQRSwsLGhBN+V/V3f/8JKOj8rO8Xq9hEIhcrkc9Xpdi8W5XK5VgnGbZQapQjApJaOjo7z2ta8ln8/zjW98g2w2SygUIhAIkMvlEEKQyWQAdLqq2p/NZhkbG2NyctL4/w2GHcIYgNsY5e9XcgrJZJKBgQEtC6F876oaWKECwioAHI1GyWazOhisOn7B1i4gpSRaKBT4gR/4AWKxmDZEg4ODQHOyL5fLOv9fic/Zts3+/ft10dhdd921e2+WwdCFGANwm6LE39qbvKfTaSzLYmxsjFQqpQu9vF6v7kgdDWAAACAASURBVPlbKpUAdAcu1fRdpWuqjmHq/81QPYOhWYg2Pj4ONGUpHMchGo2STqcBdD2AZVn09fVpUTpVMGbcPgbDzmMMwG2Kustvb/I+ODhIIpFgcnKS8fFxwuGwzvuvVCrUajXt31eKn0qiQaVnqkDtdvB4PHqVMTQ0pFcki4uL5PN5wuEwvb29FAoFSqWSzvpRonVqxWHy/g2G3cEYgNuUZDJJNpvVPvXe3l6Ghobo6enBsiwSiQSVSoVIJMLi4uKqyV/Rnhmk+v9eDSqI7Pf7uXTpEqVSieHhYUZHRzl37hxLS0sMDg7qVFC/38/Q0JCuQxgYGFhVvGYwGHYWYwBuQ7LZLJcvXyafz2tf//LyMoVCgf379zM6Oko+nycWi5HL5XSjl7UBXeXv324h2Fop6FqtRjweZ3x8nFQqxdmzZykWi0SjUcbGxvD5fORyOQBGRkZwuVw6BlCr1UgkEsbvbzDsIsYA3IYsLCzoAG6hUNCTd6VSIRgM6v1DQ0OUy2V8Pp/W5mnnalQ/oZnaqeoEVCex/v5+UqmUDiIvLy9TqVTwer3s27dPv6ZyR6VSKd1tTAnVGQyG3cEYgFuAtdk8WzVHaZd2UJN4vV7Htm3K5bLOxZ+bm8NxnKvO7d8Mt9utq4NVPUEmk1lVAyCEoFAoMDs7y6FDhwB0gZcq8lLBZ4PBsHsYA3CT057NU6lUePHFF3nqqacYHR3l6NGjOrOm3Uik02kymYxutKI0//1+v+67q1Q3pZSrMnyupon7WlQXMZ/PR61WQwhBPp/XGT6qmli5epLJJA899BAA09PTQFPqoVqtmoIvg+EGYAzATY7K5snlckxPT+Pz+QiHw2QyGb761a8yOTmpG7oPDAxgWRaZTIalpSXcbreWdq5Wq/T09ABNV1AikdATdTAYXKUI2q4P1B4H2Aq1klCFZSpdtF6v6wrjSqWis4p6enr0SkZJVRcKBUKhkCn4MhhuAMYA3OSoVo5zc3P4fD58Ph+2bZPJZKjX6+TzeSYmJhBCMDc3hxACx3EIhUKUSiVs29b++Ewmo91ISmunWCwSi8WoVqtks9lVr61WAltN/i6XS2fxKC1/eKlmQAWZvV4vXq8XaK4W9u7dq5/DZPsYDDceYwBuclQrR9UuUTVHUc3Ua7Ua8/PzWrLB5XKt6vjl9Xq1oJsKvkopSaVS2kWUyWT0JH0tsQBlINpdSSqrSLmEpJRUKpVVMYmhoaEdfa8MBsPVYQzATc7o6CjT09O4XC7dxB2ad9DKKCi/f3u6pnLdKK0f9X+hUKBQKOjn93q9q4q/lLtnrerndqhWq3g8HmKxGEIIyuUytVpNZyQpyelYLIbP59M9fvP5/LYD3AaDYefoaD8AIUSPEOITQogXhBCnhRCv7OR4bkZUK8dIJKIn8lAopDV2VCtHtU/54NWPMgDtvnl4Sce/Wq1qyQclBHctk796TlXBq0TglJS0y+VicHCQ4eFh3G43vb29NBoNvv3tb1Or1QiHw9RqNaanp69wRRkMht2h0w1hfg/4vJTyTuBe4HSHx3NTEovF2LNnD8ePH9e6Pn6/X6dVKkll5fZpT8PcyH+/2QR/rVlAjUaDer2+ytXUns8fDAa1K0hJQCgXkZKN9vv9emVgMBh2l465gIQQUeC1wDsApJRVoNqp8XSKrXL82/VzGo0G/f39ZDIZfD4f+XyeRqNBqVQiGAzi9XrJ5/NUKhX9+O1m8FwvKn6g2kqqLB+3283ExASJRELn9g8NDREMBrl06RLhcHjV83i93lUuKoPBsHt0cgVwB5AA/psQ4ttCiP9XCNFVrZ5Ujv9GLpD2/fF4nEQiQTqdJhaLUa/XKZfLDAwMEI1GEULo4DC8pMOvfu82QggsyyIYDBKNRunp6eHo0aPs27ePgYEBDh48SDQaxe/3Mzw8jG3bCCGuMACm45fBcOPopAHwAPcBfySl/B6gCPzS2oOEEO8RQpwQQpxIJBI3eoy7Srti53oukPb9lUqFwcFBAoEApVKJkZER7r33XqLRKOPj45TLZe1rtyxLB3Tb/f6bcbWGYu3xjUaDUChEb28vIyMjDA8Pc//993P06FE9nomJCfbs2aNln++77z6tMKoaw1cqFUZHR69qLLcqt/O1bbg16GQW0BwwJ6X8Zuv/T7COAZBSPgo8CnDs2LFrc07fpKgc/3baXSDt+23b1lIJlUqFiYkJpJSrVD1VwZUQgmq1elWulKtxE6kYg5J7tiwLIQQjIyO6FkDdxW+V3x+JRLq2AOx2vrYNtwYdMwBSystCiFkhxGEp5TTwMPDdTo2nE6gcf6XZD6tdIO37fT6fvpv3+/362GAwSDabJRqN4na7icfj+Hw+MpkMp06duuaA7nq0xxPUpN/T06PrCaLRqNYa2u5dvCkAMxg6R6frAP418JdCCC9wHnhnh8dzQ1E5/rC+Bk77/ng8zuzsLLZtEw6H+c53vkM2m8Xr9er+uaVSibm5OTweD8lkcseDv36/n1qtpp9XVRQrbR/HcdizZw8HDhwwk7rBcAvQUQMgpXwWONbJMXQSleO/kQskFosxOjrK6dOntW6/lJJisairavP5PJZlUa1WdfN0ldO/Fe1qodvBtm19x1+pVLTUw6FDhzh69Kgedzab5fTp06a4y2C4yen0CqDr2cwFolJAh4aGmJiY4MKFC1q/3+/3Mzs7u0ryIZlMAmj1z63aN17tCqFer+uag0AgQF9fn872aZ/81/Yinp6eNm0dDYabEGMAbhLWqwdY29e3Xq8TCARIJpNYlqX18lXBl6r+VYHg3aBYLBIMBrnzzjvp7e29YmJfrxex2m4MgMFwc2EMwE3ARnfNtm0zMDBAsVgklUqxsLBAqVSiUqno7BtoBmTbawCuxq1ztQQCAUZGRpicnFzXtbNVZpPBYLh5MAbgJmCju2bV1F2leqrJX6V7qobrlUqFarV6zRo+W+F2u4GmodmzZw+Dg4Mb9urdKrPJYDDcPBgD0AGy2Sxnz55lYWEBIQS2bbNv3z4cxyGVSmkNf2i2baxUKiSTST25ezwenRJaq9W05PNuST5IKbXKpypK24itMpsMBsPNw5bln0KIfyWEiN+IwXQD2WyWZ599ltnZWSzLwuPxkM/nOXXqFDMzM9TrdX1Xn81mKZVKuqJXSkmj0dCFVuFwWAdlPZ7ds+UqxmDbNsvLy6ysrHD69Ol1VTtVZpNlWRQKBSzL6ooAsBDiS0KIezs9DoPhatjOrDEMTAkhvgX8KfD3crcczF3AwsKCLpZSPvze3l5mZ2d1V61UKkW5XNbKno1Gg/Pnz+vc/lKpRC6Xo9FoMDExwbFjx8hms5w/f14Lw42NjV33pNvuUqrX65RKJbxeL0NDQ1q3aL3JvRuKu4QQLwM+IKV8W2vTLwC/K4S42Nq+2LnRGQzbY0sDIKX8D0KIDwKvo1mo9YdCiI8DH5FSntvtAd5uFItFHMfRUs7Q9JtblsXi4iJf/OIXmZ+f135+y7Ko1+vE43Hm5+e5cOEC1WqVyclJQqEQZ8+e5eTJk3g8HkKhEP39/TiOsyOpl0pPSDVyUZo+SrcIujq758uA7l8hpfwW8I+EEG8GPi+E+Fvgt6SU5U4N0GDYim0pgLXu+C+3fhwgDnxCCPFbuzi225JQKLTKhw/gOA62bfP0008zPz+PZVmk02k94ZdKJV544QWWlpaoVqvUajUuXLhAsVjU3cAKhQLJZJJTp06Rz+fx+/3Mz89ve1xCCN2vV2FZFl6vV7d09Hq9BAIBvSrwer0Ui8WdeWNuPV4H/Hr7BtHMvZ0G/ohmlfsZIcTbOzA2g2FbbCcG8HNCiGeA3wK+BtwjpfxZ4H7gzbs8vtuO0dFRAoEA5XKZarVKtVqlVCqRSCTI5/NEo1HtxonFYlQqFVZWVggEAuTzeYQQq1oqKndQOp2mWq1qd1GtVqNUKm06Fo/Ho5VIVV2BUvlU7imv14vb7SYQCGg553Ytom7N7pFSPi+l/HH1vxDiH4B54HeBMZp9Lh4CXiGEeLQTYzQYtmI7MYB+4EellBfbN0opG0KIH9mdYd2+xGIxjh49yte+9jWefPJJcrkcPT09nDlzhvn5eRzHIZ1O6w5fuVyOTCZDpVLB5XIRCAR0KmixWKTRaOgG7CsrKxSLRYQQLCwsMDo6ysjICGNjY+uOxefz4Xa7taSD4zh4vV56e3uRUpLNZnXHrt7eXkqlEoFAgHg8jm3bpNNpwuEwJ06cMJIP8F7g1DrxsX8thDCd7gw3JduJAXxok33mwt6Eubk5pqamSCQSDAwMcPz4ccbHx8nn88zMzHDkyBEqlQqf//znee6550in00gpKZfLOs9fGYJCoYCUklKpRKlUwrIsnRmkegKruIHK2MnlcjzxxBM89NBDVxgBFVuAZp6/usuPxWIMDw+Tz+cZGRkhnU5rbaF9+/YRj8dpNBrUajX9PCrds5slH6SUJzfZ/cM3bCAGw1Vg6gB2ibm5OR5//HHq9ToLCwt885vf5HOf+xzvfve7mZubo6enh2g0yte//nVSqZSWVy4UCrpblsfjwbIsfD4f2WwWn89HqVTSmjyK9r/byWQyADz//PPccccdetKWUmJZFrVaDcdxGBkZYWhoCJ/Pp4PU9913HwsLC0xOTq7K51dKn6dPn9ZjAyP5sBlSyvOdHoPBsB6dbgp/2zI1NUW9Xue73/0utVqNkZERPB4Pjz32GC+++KKWSzh58qT24ddqtVUSD/V6nXw+z8rKCpVKRTdR3w4ul0unbs7MzLC8vHxFk3ilBprJZKhWq0xMTHD48GHi8bgOJG/UraxYLF4RNO7yoLDBcMthDMAukUgkWFhYIBQKEQwGEUIQj8d1ta/K2lleXqZcLlMqlbTWvmq80t7hCza+018PNdGrwHB7RpByGan4gTpO/Q6FQltO8EryoZ1uDgobDLcixgDsEgMDAyQSiVX5/pVKhaGhIeLxOJlMhueee47e3l4t82BZFo1GY5XUguM4emVwNShDonL4U6nUqv3KjaTy+y3LWtWTd6sJfnR0lEql0rX9fA2G2wFjAHaJ48eP43a7SaVSunq3WCwyMjLC4cOHeeSRR6hUKrjdbnp6eojH45uqeF5L8bWUUrtu1vYGqNfruN1uotEow8PDeL3eVbINW03w3Sr5YDDcTpgg8C4xPj7Ou9/9bh577DEWFxcZGhpicnISt9uts4F+8Ad/kFqtxr333svJkyd5+umn9V379aptKNdOrVajXC7TaDTweDzavaRSSpWL6ejRo4yPj+vHb9WtTB1jJnyD4dbFGIBd5Pjx4wB84hOfYHZ2lkajwVve8hYAHnvsMZ588kmmpqYYHh4mGAwSj8f1iqFd23+7qMldTeoul0uvAJTfX/XvlVISCASIRCJYlsXCwgKRSMRM8AZDF9FxAyCEcAMngHkp5W1VWDY3N8fTTz/Ny1/+cg4dOsTzzz/P+9//fl31qxQ9z507p/3+Pp+PRqOhK4I3k15eiwraqniCytEHCAaDQFPyQeX8Syl1kHhoaMikcBoMXUbHDQDwfwCngWinB7KTzM3N8Qd/8AckEgmCwaDW/1cyDeruWnXKcrvduvCr0WhQKBSuWt+/0WjoegJV1evz+RgaGmJsbAy/36/z/wHt1w8EAszPz+vtBoOhO+ioARBCjNOskvx14N92ciw7iSoCSyaTDA8P8+STT/Liiy/i8Xio1+s6FVTJOyiffCQSIRgMUq/XdRHX1VCtVqnX6zqbSK0wYrEYg4ODuN1uXWBWq9W0sQkGg7rQzGAwdA+dzgL6ME0d9d1pZdUhPv/5z2ttn5MnT3Lp0iUsyyKfz+u7eimlrrpVGTrRaBSv10skEtFNXtobvSihts2o1+s6c8fv93Po0CGOHj2qJaeHh4d1oRlAOBzWInBrM4UMBsPtTccMQEtIbllK+cwWx71HCHFCCHEikUjcoNFdO3Nzc3z5y1/G5XJx8OBB5ufnWVpaIpFIaE0dNak3Gg2q1SqO4+A4Dv39/ViWxcGDBwkEArjdbkKhkJ74t+sSEkIQjUaxLIs777yTeDyO1+vFcRyt59Pb24vP58Pn8+FyufQxhhvHrXZtG24/OrkCeBXwBiHEBeCvaTbT+Iu1B0kpH5VSHpNSHhsYGLjRY7xqpqamGBoaQgjB5cuXWVhYWFV5q1xAKltHtXgMBoPkcjnK5TKXL18mGAzidrt1dfB2Udk/9XqdpaUlzpw5w969exkfH0cIQSKRoFar6aIuFXuwbdsUcd1gbrVr23D70TEDIKV8v5RyXEq5F/gx4H+0tde7ZXnxxRep1Wo89dRTfOUrX8HtdjM4OKgnZo/Ho/9Wd/jBYJBSqcT58+fJ5XIA2l+/laY/rHYNKS0hx3EIh8OcPXtW6/2ohi5K9E1lGNXrdWq1GkNDQ7vzphgMhpuSmyEL6LZhbm6O5557jpWVFZ3C6TgO8Xic/v5+isWizrTx+XxajkGJtFWrVYrFIisrK1qobT1U4Fix9u9arUatVtNictlsFtu2GRoa0k3ko9EojuMQCoWIRqOEQiHy+fzuvkEGg+Gm4qYwAFLKJ4AnOjyM6+ZjH/sYMzMzpNNp3fhduXAGBweBppFQE36lUlmlt6N0eZSbSPXfbf8NL034qqBrrYtIZfbYto3f7yeTyXDHHXcQj8f16iASiVCpVIhGo4yPjyOl1CmpBoOhO7gpDMDtwNzcHJ/+9KeJxWIEg0FOnTpFLpdDSkm9Xsfv95PNZnUaZqlUuuIOXzVyWY/2Y91uN/F4nFwud0XuvnIzxWIx/H4/b3/724lEIgQCAR18tiyLarWqu4uBUfI0GLoRYwB2iKmpKe3WyWQy9PX1Yds2tm1Tq9VYXl6mWCzqPr9XU+G7HpZl6boCKSUej0dXAAcCAcbHxxkfH+fee+9lZmaGWq3G4uIigF59BINBfD6fLgibnJzcibfCYDDcIhgDcA2s1+oxkUhw55138uSTT+L1eqnX6wQCAWzbJh6PMzIywqVLl1hZWbnu15dSsrS0pOUeVBxB9fe99957OXr0KD6fj0KhwMDAAJFIhEKhoIPE6u5fSkmlUmFkZGQH3hmDwXAr0elCsFsOVeVbKpUYGhqiVCrx+OOP43K5OHz4MB6Ph2w2q+/4o9Eod9xxB4lEgmq1ipRyWwVd6+H3+4nFYni9Xl24ValUdL8AIQS2bXPu3DmWlpYYHh4mk8no5vAvf/nLGRsbIxaLEY1G8fl8HDx4kAMHDmBZFtPT02Sz2R1+xwwGw82KMQBXydTUlO7n63K5iEaj9PT0IKUkl8vpNoput1sLrZ07d04XWSm3zbWwtkELoBvFqNx+t9tNNpvVlciveMUriEQieL1eQqEQExMTHDhwQNcAbNTy0WAw3P4YA3CVJBIJ3c9XEQ6HkVIyPDxMf38/qVRKZ/GkUind8QuaQdprXQGoxjKNRgPHcVbtU6mhHo8Hv9/P4cOHefnLX87TTz9NPp+/wngUi8UrzsP09DUYugsTA2ixnl+/vUGKYmBggEKhQDTaFC9NJpM899xzVCoVlpeXOXfuHC6Xi1qttipFc2FhgUAgoHV41rub3w5CiFWPbTcs0Czq6uvr0+4n9doqw8fr9VKtVhFCXGEATCaQwdBdmBUAG/v15+bmrjj2+PHjZDIZcrkcy8vLfPWrXyWdTrN//35OnTrF/Pw8mUxGyzGr9MtqtUoul9MB2+2iqoaVtr+681cBX0AXjamU03A4rCf3cDhMsVi8on3jfffdp+MIpqevwdCdmBUAq/36gP49NTXF+Pg4c3NzfO5zn+Nb3/oWUkruuOMOfD4fzzzzDD09Pdx7770888wzWmK5WCzqTCA14asJWhVitRd2rVfQpXT71eNUd69gMEggECCZTGoDUy6XdX1BT08PbrebSCQCoLOA1uvuFYlENm35aDAYbm+MAaDp11+rgxMOh1laWmJubo6PfvSjnD17lng8TqFQ4LOf/awuppqcnOTMmTOcPHmS/v5+/H4/uVxOT/pqElcUCgUdB1DB4Hq9rrWB2gPE7UZCCKGLviKRCD09Pbq+wOv1Mj4+TjweXyUfncvlyGQyPPjgg+uet2n5aDB0N8YAcKVfH166c56amtJ32y+++CIXLlwAXpq0U6kUMzMznDlzRufdu1wuHQSWUq6a2JWbZi3ruYVUcxglJ+H3+wkGg1QqFe6//36OHDnCpz71KSqVCvF4nPHxcYaHh7X4WzAY5MEHH1w3lmEwGAxdbwDm5uZIJpN85StfYXBwkHvuuUfr5zz44IN89rOfJZVKMT09zcWLF7XQmuM4BAIBreSpRNyUW0Y1f2m/i78ahBB4vV7tw1evFQwGCYfD9PX18Q//8A/09fVx4MABYrEYxWKR+++/X8tLv+lNb9qFd8xgMNwudLUBUMHfnp4eHn74YZ5//nm+9KUv8fDDD/PII48wPj7OwMAA586d4/z58zpgWi6XtQSD4zhawhnQd/zhcBjbtqlWq3i93nWlH9a6eFR8AF7K6hFC0NfXRywWY+/evcTjcWZnZ5mamqJcLvPKV75S6wcFg0Gee+45+vv7GR4e5tFHH900o8lgMHQ3XW0A2oO/0WiUhx9+mFwuRzAY1BPm8ePHmZ2dpVqtXtE2cb1UTuX+Ud226vW6zthZm7uv4ghCCPx+v9bqV+0iBwcH6evr0yuLeDxOqVSiv7+fUqnE/v376evrY2lpSXcby+fzDAwMEAgECIfDFAoFHn/8cW3QDAaDQdHVBmCz4K9ifHwcn89HNBqlXC5TqVR0M3Wl4b9WqllN4GoSblfsVNk9Ki6gXEY9PT24XC6OHDlCMplkbm5OB4aPHDmC4zgEg0Esy9L9fvv6+ggGgwwNDeHz+Thy5Ajf+c532Lt374YZTQaDwaDoagOwWfC3ndHRUZaXlxkbGyORSJBIJHRbR1gt1axSP5XMQjgcJp/P4/F4tAtJpWkODw8jhGBxcZFEIoEQQtcQ3HPPPbzxjW/UPYUfeOABent7eeKJJ5iYmOB1r3sdZ86coVQq4fP5uHz5MmNjY/T29q5bqdxu1AwGgwG6vBCsvair0WjotMnjx48zNzfHJz/5SR599FH27NmD2+3Gtm3cbrdW3lR9ezdicHAQn8/HnXfeyeTkpNbdUe4g27Z1oLdWq1GpVCgUCng8HmZnZ3VLyZGRERYWFrBtm4ceeoi7776bQ4cO8cADD+Dz+VhaWmJgYIBHHnmEQ4cOXdHYZT2jZjAYDF29AhgfH+eRRx5hampKT6KHDh3ic5/73KqsoOPHj7O4uKgn6OHhYcrlMvl8XjduX4tlWaysrBAOh/nud7+rpZhVf+DLly8zMzOjC8aklKuqd8vlMl//+tdxuVzs27ePRqNBT08PpVKJTCYDQG9vL0eOHGFsbGyVj//xxx/Xz1MoFDatBTAYDN1LVxsAQDdOgaaf/LHHHuPs2bOEQiHC4TBTU1M88MADvOENb+BjH/sYtm3rPr8+n+8K9Uzlt1dFWtVqlVKphOM4eDwe8vk8xWJR1wKoGAI0BdpcLheVSoVwOIwQgtnZWS5evEh/f78uAHvb2962ymi15/qvZ9RMLYDBYFiPjhkAIcQE8OfAMNAAHpVS/l6nxjM3N8djjz2m1TRt22ZqagqPx8Ozzz4LwLPPPks4HNZul2w2u0rZs71/b7v8g9rnOA6FQkEHkGG1wWg0GrrArFQqEQgEWFlZIRaLEQgEyOVypFIpgE1z/NuNmsFgMGxEJ1cADvA+KeW3hBAR4BkhxBellN/txGCmpqbIZrPU63VmZ2e1tn+tVsO2bZaWlnRVrs/n049T+j+AduUo+YdgMEgkEtEtGOHKit/2/5XxUMaiVCrhcrkYGhrShWV33323yegxGAw7QscMgJRyEVhs/Z0XQpwGxoCOGIDp6WnS6bQWZsvlciwtLelq3nb5Btu2dSqolBKv16u7cqlJ3LIshBAkk8kt+/8qI6Aer7KEVJ9e27ap1+scOnSIyclJk9FjMBh2hJsiBiCE2At8D/DNTo0hnU4zNDTE7OwsyWRSb3ccZ1Wmj3LpqDRQn8/H+Pg4yWRSV/6qbmBXo/kvhCAYDBIKhfSEH41GGRwcRErJnj17SCaTDA0NmYweg8GwI3Q8DVQIEQb+Bvh5KWVunf3vEUKcEEKcSCQSuzaO3t5eXWilXD3KHbOeAVB37fV6nWQyiWVZ+P1+nSaqArvbQa0Yenp6uOeeexgZGdGaP41Ggz179uD1evnGN77BZz7zGVZWVtbtVWC4tbhR17bBsBHiWoTKduzFhbCAzwB/L6X8na2OP3bsmDxx4sSOvb7qAjY9Pc03v/lNHMfh/PnzLC4u4na7sSyLZDKpg7OtMa/qwqVWAY1GQ3f7qlQq22r64vF4dFC5r69vVd9gy7I4ePAgDz30EM888wzPPPMMfX19vOlNb9JidUbeYWcRQjwjpTzWidfe6WvbYGhno2u7k1lAAvgIcHo7k/9Oo4Tg6vU6MzMzhMNhZmZmdDaO4zha9kGtBlQhl/LpezwevWrIZrOUy+WrUv6s1+t4PB4ikQj33nsv1WqVZDLJ3XffzdLSEvF4nN7eXjweD4cOHeKhhx6iv79fP94Egw0Gw/XQyRjAq4C3A88LIZ5tbfuAlPKzN+LFlRDcqVOnkFJSqVSoVCosLi7qnH3VAEbd2asmLIVCgVqtRigUwuPxUCgUdPD3agyACjgfOnSIaDSKy+Xi4MGD3H333czMzDA8PMzS0hKVSoXXvva1qyZ/I+9gMBiul05mAf0DsH1H+Q6jhODm5+e5fPkygUBgVdtGgHK5TK1Wo16v09PTQzweJ5fLYdu2zvVXhmO9Ji8b4fF48Hg8jI+P4zgO8/PzhMNhUqkUx44dIxgM8o53vEPf3X/yk5+kVCqteg4j72AwGK6XmyILqBMoITjVwater3P58mXdwF1l/6guX6lUSrt+/H6/9vO3F3VtW2aIwgAAE3dJREFUtQJQDd69Xi979uzB5XJRKBQol8u8+tWv5lWvehVut1vr97fHKM6fP8/dd9/N5OSkkXcwGAw7QtcagOPHj/P444/rfP65ublVVbter5dqtYpt23rS9vl8+P1+pJT09PRQLBa1wiew7uSvKoVVnwCXy8XIyAgul0u7kLxeL47jEIlE8Hq9TE1NAehmNXfddRfBYJCTJ09SLpc5dOiQkXcwGAzXTdcaAKWZc+nSJWZmZkgkElqMTamDqiYr9Xpd/x8Oh4lGo/T09ADNjB+Xy3VFsRigt1uWpQ2N0gNSTV48Hg+vec1rCIVCnDlzhgceeIClpaVVzWoA9u3bp/X/TatHg8GwE3S8DqDTHDhwAI/Hw+joKAMDA4yOjuI4jvbxK1TVbzabZXFxkZWVFWzbZnBwkMHBQfx+v77bd7vdeL1ePcFXq1U8Hg8TExPs3buXYrGIlBKXy8Xk5CSZTIZqtUo2m9W+/XaDpAiHw5h8cYPBsFN0rQFQaaDBYJCHH36YUCjE2bNnOXv2LL29vfT29q4SepNSrtL6KZVKelVQKpV07n44HNa/VSGZy+VieHiYgwcP4vP5iMVivOIVr+Cuu+4iFoshhODChQtYlqX7EagYRTsm8GswGHaSrjUAysVSrVb59re/zeLiIpOTk1qLx3GcTQO61WpVB4cLhYK+q3cch0AgwPDwMNFolL6+Pvr6+igWizqQfOjQIer1OuFwmIMHD+LxeFhaWuLuu+/WxV2bNasxGAyGnaBrYwCJRAK3280TTzzBCy+8QLVaxefz4fV6icViZDIZnR20HspQqMwgl8uFz+ejVqsRjUbJZrPk83mEEMRiMdxuN6lUisHBQSYmJnSDl3q9zv79+3nDG97Au971Lv38RtffYDDsNl1rAAYGBvjMZz7D/Py81ujPZDIIISgUCti2venjVWBYIaXUchDz8/PU63X8fr+e/FW6aV9fH36//4qUzh/6oR+64jWMrr/BYNhNutYFdPz4cV588UUajQbFYpF0Ok2xWCQQCFAoFMhms5vq+dTrdRzH0f8r+Qj12+v16j7CQgj6+/vp7+/n9a9/PR/60IeYmJhgaWmJYDBoNH0MBkNH6NoVwPj4OHv37uW5556jWCyuatlYKpVwu91aqgGaPv/NYgIqOAzoAjJAG5h8Pk8ikeBv/uZvcLlcvP71rzeTvsFg6ChduwIAuOeee7h06RL5fJ5CoUAulyOfzwPoTB6Px6Ozf7ZCGYFAIEAoFNLCcaVSiWq1SjAYZM+ePTz11FP82Z/9mZF0NhgMHaVrVwBzc3OcO3eOUqlEvV7Xd/tqslfpnVej8aO6g/X29tJoNAiFQkBz9WBZFt/3fd/H8PAwpVKJRCJh1DwNBkNH6doVwNTUFPPz8wQCAZ3D73K5tBGAK/v3bge1Cujv78ftdiOEIBQK8bKXvYx8Pq8zjqrVqinqMhgMHaVrVwCJRIJkMonH48HlcmkBuHba3T6q+ctW9PX1UalUmJubY//+/YyNjbGwsEA0GiUUClGtVjl16hR33HGHKeoyGAwdpWsNgMvlIp/Pax//2slfHaOMgJJ02Oo5I5EIhw8fJhwOs3//fpaXl+nt7aVSqejUUlVJbIq6DAZDJ+laAyD/V3t3F9vWeR5w/P+QFClKlEmJlFR92rJjO5Ht2AhED/CCudnc2Vs2Z0M2oDWCGWuA7CZX20W35GLBWmBBt11s2LDBHQI0QLtiQGYoGOy0MTakF8lseY7t1VkcK/5QqQ+bsj5oiaJJiu8uyHNG2bIrJZIOyfP8biRSNPlIPocP3+d9z/sYQ3t7O9evX7dX75TzeDz2p/6VTABbPYBv3brFyMgI9fX1TE5O0tvby5YtWxARhoeHERGefvppenp6tP6vlHKUaxPA3bt36ejoIBAI2Ffzlivf5x+K6/79fj8isuxFYlYzmVwuZ7eRvHXrlp08XnrpJQ4fPgwUdxttaGhYp99MKaVWxrWTwNPT04TDYTZt2kQ4HLY3cXsUq0cAFBvClG/0Vv6Y8vui0SipVIqpqSnd00cpVXFcmwBaWlpYXFy0J2bT6fRDpSDrgi6fz2dv9WCNBBoaGpasILJKQFZLyWAwSDAYJJfL2W0e9cpfpVQlcbQEJCJHgL8FvMA/G2Pe3KjX3rFjB5lMhqamJmD5JZ/Wfj9er9e+be0SWigUlswTWEs+/X6/PQIYHx8nEomwdetWbeKiVsVqB5pMJvF4PNy9e5ezZ89y+fJluxdFLpdbdvFCLevo6OD555935Qcon89HKBQiGAzaS9UjkQg9PT12T/PGxkY6OzsJh8Mrek7HRgAi4gX+AfgNoB/4hoj0b9Trx+NxRkdHGRgYYO/evUtKOeWs6wKsC8T8fj+5XM5OAlCcMLZWE2UyGXK5HOFwmGAwyObNm7lz545e9atWzOpVYW1J8t577/H222/z0UcfMTY2RiqVYmFhwXVv/lD8UPXOO++48nzK5/PMzMwwMTFBKpUil8sxMTHBpUuXGB4exuPxkMvluHr1KrOzsyt6TidLQPuBYWPMdWNMFvgR8MJGvXh3dzfbtm0jHA7bWzs/ijWRu7i4uKRpfDAYBIr/MeFwmGg0am8hnU6nOXDgAC+++CJbtmyx+/wq9YuUtwP9/PPPyWazLCwskE6ngeV7T7vJ7Owsn3zyidNhOObBCkQ2m6VQKDA9PW33LR8bG1vRczlZAuoCfl52OwH80oMPEpFXgFcAent71zSAHTt2kE6nuXjxIl6vd9nloOWsN3ar3m91BYtEIjQ0NNDc3EwoFCIcDnP//n0OHjxILBajUChw+/btNY1dVb9HHdvJZJL29nag+GaXz+fJ5/Mr3pOq1lmLKdzswR0LrOoDgN/vf6ib4KM4OQKQZe576Og2xpwwxgwYYwbW+srZ7u5uPvjgA65evbqqbR/q6uqor68H/n/9vzU30NLSYjeCv3btGrB8K8dEIsHJkyc5ceIEJ0+edOWQ1u0edWyXtwMNh8P4fD58Pp89z+R2Ho+HTZs2OR2Go0TErlp4PB68Xq/9npTNZu19yH4RJxNAAugpu90NrGzcshYvnkhw7tw5urq6lt0G4lGsuYL6+nqi0SjBYJCFhQX8fj9dXV20tLQwPz9PW1ub3dLxwWWf5TXe9vZ20uk0g4ODmgQUwJJ2oNu2bcPv9xMMBu1rR9yeBMLhMP39GzZdWHGspebWtUrWwpPm5mbu379PJpOhs7NzRc/lZAloCNguIn3AKPB14NiGvfjQEIuLi4yPjxONRpmZmSGbzS5bBvJ6vRQKBXw+n73bZ2dnJ4VCgampKYwxdHV12V3A+vv77R1BGxoaHmrlWF7jBeyvujuogqXtQOfn5zly5AjxeFxXAaGrgB5cBdTa2mqvArI6Em7evHnFq4AcSwDGmLyIvAr8mOIy0LeMMVc26vWTySRjY2M0NjYSjUYZHx9/ZBtIa5mn9QcOhUJkMhnm5ubo6Ojg5Zdf5sMPPySfz9Pe3k5HRwder/eR6/3La7yWUCik8wTKpu1A1UZw9DoAY8wp4JQTr93a2srZs2fp6OggGo3S2dlpL62z+gNYs+vWkMvj8dDb24sxhnQ6zZ49e3jttdeIx+McOnSI06dPc+HCBaanpxkYGHjsa8/NzS2pYy43T6CUUuvJtXsBxeNxTp8+zcjICIlEghs3bjA/P29Ptnm9XiKRCIFAAI/HQ1tbm93fd9++fTQ3N7Nr164ltf1sNsuzzz5LKBRibm6OwcHBZUcB8XicwcFBAPuxMzMzHDx4cEP/Bkopd3PtVhDd3d0cPXqUjz/+mGvXrtHQ0EAgEFhy0ZcxhqamJnsriL6+PmKxGF1dXTz33HNLluSV1/WtVQqRSGTZ9f9WjVe3h1BKOcm1IwAo7su/adMmZmdnmZmZwev10tjYiM/nQ0Ts9cadnZ3EYjF8Ph+RSITZ2dmHSjarretrjVcp5TTXjgAAzp07x2effcbc3BwiQiAQIJ/P25PBTU1NBAIB9uzZQz6fJ5VK0dzcTF1d3UNLO8vXblu0rq+UqmSuTQCJRILz588D2HX/dDptX1QRi8Xsev7IyAhPPvkkfX19zM3NsXv37odKNuVrt3XbZ6VUNXBtAhgaGqKlpYXGxkZyuZzd/tG6DsDqFXD8+HF27txJT08PsViMffv2EY1GH3o+resrpaqNa+cAkskkfX19TE1NkUgkmJ6eRkQwxtgrf3bs2EF7ezuRSIRsNktPT89jV/hoXV8pVU1cmwBaW1vJZDIkEgkKhQLd3d3cvHmTVCrFE088QX9/P5cuXVqSBPTKXaVULXFtCSgej3Pv3j174vfKlSukUim6u7sJh8Nks1mam5tpa2ujUCgQCoWW/PtQKEQymXQoeqWU+vJcmwAAe51/b28v9fX19qf8bDbLzZs3mZqa4sKFC3g8Hl3ho5SqOa5NAENDQ/T19bF3714mJyfJZDJkMhkmJye5c+cOyWSS8fFxAoEAExMTdnlIV/gopWqFa+cAkskks7OznDlzhitXrlBXV0ehUGB0dNQeEYyOjnLs2DH8fj/pdNpe4dPa2vrQDp9KKVVtXJsARIRTp05RX1+P3+9HROy9flKpFLFYjPb2druj1/z8vDZ2V0rVFNeWgESETCaD3++nubmZhYUFFhYWEBFyuRx1dXXs2rUL0Hq/Uqo2uTYBFAoFnnnmGXvdvzGGxsZGvF6vvd3zli1btN6vlKpZri0Btba2snPnTruzTlNTE8lkkkwmw/79+/F6vQwPD7Nt2zat9yulapJrE0A8HmdsbIz+/n5u3LjB4uIira2tHD58mO3bt1MoFLh9+7bW/ZVSNcu1CaC87+rWrVsJBALs3buXWCwGaN1fKVX7HEkAIvJXwG8DWeBz4A+NMTMbHYe1d4/Vocvv91MoFLRDl1LKFZyaBH4f2G2MeRr4DPgzh+IgkUgwNDTEvXv3uHz5Mp9++qnu5KmUcgVHRgDGmJ+U3fwv4PeciCORSDA4OEgkEuGpp56yP/nH43F981dK1bxKWAb6TeC0Ey+8mj6+SilVa9ZtBCAiZ4CvLPOj140xg6XHvA7kgR885nleAV4B6O3tXdMYV9vHV6m1tJ7HtlIrsW4JwBhz6HE/F5HjwG8Bv2aMMY95nhPACYCBgYFHPu6LsPr4Wvv7g67+URtnPY9tpVbCkRKQiBwBvgUcNcaknYgBtI+vUsrdnJoD+HugCXhfRC6KyD85EYT28VVKuZlTq4CecOJ1l6N9fJVSblUJq4CUUko5QBOAUkq5lCYApZRyKU0ASinlUpoAlFLKpeQx12BVHBFJArfW4aljwOQ6PK/T9Pdanc3GGEeuAlzHY3u1quGYqfQYKzG+ZY/tqkoA60VEzhtjBpyOY63p76VWqxr+tpUeY6XHV05LQEop5VKaAJRSyqU0ARSdcDqAdaK/l1qtavjbVnqMlR6fTecAlFLKpXQEoJRSLuXqBCAiR0TkqogMi8ifOh3PWhKRmyLyP6XdVs87Hc8XJSJvicgdEflZ2X0tIvK+iFwrfW12MsZaIyJviMho6di5KCK/6XRMUB3na7Wdd64tAYmIl2JD+q8BCWAI+IYx5hNHA1sjInITGDDGVNp65FURkV8B5oC3jTG7S/d9F5gyxrxZeiNoNsZ8y8k4a4mIvAHMGWP+2ulYLNVyvlbbeefmEcB+YNgYc90YkwV+BLzgcEzqAcaYnwJTD9z9AvD90vffB35nQ4NSTtDzdR24OQF0AT8vu50o3VcrDPATEfnvUu/ZWtJujBkHKH1tczieWvSqiFwuleAqocRWLedrVZ13jjSEqRCyzH21VA/7ZWPMmIi0Uey89mnp07RSiMgZ4CvL/Oh14B+Bb1M8H74N/A3wzY2LblnVcr5W1Xnn5gSQAHrKbncDYw7FsuaMMWOlr3dE5CTFIXTFHoirdFtEOowx4yLSAdxxOqBqY4w5tJLHicj3gH9f53BWoirO12o779xcAhoCtotIn4j4ga8D7zoc05oQkUYRabK+B34d+Nnj/1VVeRc4Xvr+ODDoYCw1p5RULb9LZRw7FX++VuN559oRgDEmLyKvAj8GvMBbxpgrDoe1VtqBkyICxf/jHxpj3nM2pC9GRP4F+CoQE5EE8OfAm8C/isjLwAjw+85FWJO+KyL7KJZYbgJ/5Gw4VXO+Vt1559ploEop5XZuLgEppZSraQJQSimX0gSglFIupQlAKaVcShOAUkq5lCYApZRyKU0ASqmqIiJ7RGRCRHY7HUu10wRQY0QkXtrEq750ZeIVPVFUjXkNOFD6qr4EvRCsBonId4B6IAgkjDF/6XBISqkKpAmgBpX2ShkCMsABY8yiwyEppSqQloBqUwsQApoojgSUqgki8p8i8rXS998Rkb9zOqZqpiOAGiQi71LsmNQHdBhjXnU4JKXWRKlF6F8A3wOOAUd1hPvFuXY30FolIn8A5I0xPyz1Uf1QRH7VGPMfTsem1JdljPmpFLfb/GPgq/rm/+XoCEApVTVEZA/wDjBpjDngdDzVTucAlFJVodSo5gcUm8HPi8hhh0OqepoAlFIVT0QagH8D/sQY878UexW/4WhQNUBLQEop5VI6AlBKKZfSBKCUUi6lCUAppVxKE4BSSrmUJgCllHIpTQBKKeVSmgCUUsqlNAEopZRLaQJQSimX+j8JgmDxsGDpBgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs=subplots(1,2,sharey=True)\n",
    "ax=axs[0]\n",
    "_=ax.axis(xmin=-2,xmax=12)\n",
    "x1 = np.arange(0, 10, .01/1.2)\n",
    "x2 = x1+ np.random.normal(loc=0, scale=1, size=len(x1))\n",
    "X = np.c_[(x1, x2)]\n",
    "good = (x1>5) | (x2>5) \n",
    "bad = ~good\n",
    "_=ax.plot(x1[good],x2[good],'o',alpha=.3,color='gray')\n",
    "_=ax.plot(x1[bad],x2[bad],'ok',alpha=.3)\n",
    "_=ax.set_title(\"original data space\")\n",
    "_=ax.set_xlabel(\"x\")\n",
    "_=ax.set_ylabel(\"y\")\n",
    "\n",
    "_=pca.fit(X)\n",
    "Xx=pca.fit_transform(X)\n",
    "ax=axs[1]\n",
    "# ax.set_aspect(1/1.6)\n",
    "_=ax.plot(Xx[good,0],Xx[good,1]*0,'o',alpha=.3,color='gray')\n",
    "_=ax.plot(Xx[bad,0],Xx[bad,1]*0,'ok',alpha=.3)\n",
    "_=ax.set_title(\"PCA-reduced data space\")\n",
    "_=ax.set_xlabel(r\"$\\hat{x}$\")\n",
    "_=ax.set_ylabel(r\"$\\hat{y}$\")\n",
    "fig.savefig('fig-machine_learning/pca_003.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see how PCA can simplify machine learning tasks, consider [Figure](#fig:pca_003) wherein the two classes are separated along the diagonal.\n",
    "After PCA, the transformed data lie along a single axis where the two classes\n",
    "can be split using a one-dimensional interval, which greatly simplifies the\n",
    "classification task. The class identities are preserved under PCA because the\n",
    "principal component is along the same direction that the classes are separated.\n",
    "On the other hand, if the classes are separated along the direction\n",
    "*orthogonal* to the principal component, then the two classes become mixed\n",
    "under PCA and the classification task becomes much harder. Note that in both\n",
    "cases, the `explained_variance_ratio_` is the same because the explained\n",
    "variance ratio does not account for class membership.\n",
    "\n",
    "<!-- dom:FIGURE: [fig-machine_learning/pca_003.png, width=500 frac=0.85]  The left panel shows the original two-dimensional data space of two easily distinguishable classes and the right panel shows the reduced the data space transformed using PCA. Because the two classes are separated along the principal component discovered by PCA, the classes are  preserved under the transformation.  <div id=\"fig:pca_003\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_003\"></div>\n",
    "\n",
    "<p>The left panel shows the original two-dimensional data space of two easily distinguishable classes and the right panel shows the reduced the data space transformed using PCA. Because the two classes are separated along the principal component discovered by PCA, the classes are  preserved under the transformation.</p>\n",
    "<img src=\"fig-machine_learning/pca_003.png\" width=500>\n",
    "\n",
    "<!-- end figure -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fig,axs=subplots(1,2,sharey=True)\n",
    "ax=axs[0]\n",
    "x1 = np.arange(0, 10, .01/1.2)\n",
    "x2 = x1+np.random.normal(loc=0, scale=1, size=len(x1))\n",
    "X = np.c_[(x1, x2)]\n",
    "good = x1>x2\n",
    "bad = ~good \n",
    "_=ax.plot(x1[good],x2[good],'ow',alpha=.3)\n",
    "_=ax.plot(x1[bad],x2[bad],'ok',alpha=.3)\n",
    "_=ax.set_title(\"original data space\")\n",
    "_=ax.set_xlabel(\"x\")\n",
    "_=ax.set_ylabel(\"y\")\n",
    "\n",
    "_=pca.fit(X)\n",
    "Xx=pca.fit_transform(X)\n",
    "ax=axs[1]\n",
    "_=ax.plot(Xx[good,0],Xx[good,1]*0,'ow',alpha=.3)\n",
    "_=ax.plot(Xx[bad,0],Xx[bad,1]*0,'ok',alpha=.3)\n",
    "_=ax.set_title(\"PCA-reduced data space\")\n",
    "_=ax.set_xlabel(r\"$\\hat{x}$\")\n",
    "_=ax.set_ylabel(r\"$\\hat{y}$\")\n",
    "\n",
    "fig.savefig('fig-machine_learning/pca_004.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/pca_004.png, width=500 frac=0.85]  As compared with [Figure](#fig:pca_003), the two classes differ along the coordinate direction that is orthogonal to the principal component. As a result, the two classes are no longer distinguishable after transformation. <div id=\"fig:pca_004\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_004\"></div>\n",
    "\n",
    "<p>As compared with [Figure](#fig:pca_003), the two classes differ along the coordinate direction that is orthogonal to the principal component. As a result, the two classes are no longer distinguishable after transformation.</p>\n",
    "<img src=\"fig-machine_learning/pca_004.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "PCA works by decomposing the covariance matrix of the data using the Singular\n",
    "Value Decomposition (SVD). This decomposition exists for all matrices and\n",
    "returns the following factorization for an arbitrary matrix $\\mathbf{A}$,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbf{A} =  \\mathbf{U} \\mathbf{S}  \\mathbf{V}^T\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Because of the symmetry of the covariance matrix, $\\mathbf{U} =\n",
    "\\mathbf{V}$. The elements of the diagonal matrix $\\mathbf{S}$ are the singular\n",
    "values of $\\mathbf{A}$ whose squares are the eigenvalues of $\\mathbf{A}^T\n",
    "\\mathbf{A}$. The eigenvector matrix $\\mathbf{U}$ is orthogonal: $\\mathbf{U}^T\n",
    "\\mathbf{U} =\\mathbf{I}$. The singular values are in decreasing order so that\n",
    "the first column of $\\mathbf{U}$ is the axis corresponding to the largest\n",
    "singular value. This is the first dominant column that PCA identifies. The\n",
    "entries of the covariance matrix are of the form $\\mathbb{E}(x_i x_j)$ where\n",
    "$x_i$ and $x_j$ are different features [^covariance]. This means that the\n",
    "covariance matrix is filled with entries that attempt to uncover mutually\n",
    "correlated relationships between all pairs of columns of the feature matrix.\n",
    "Once these have been tabulated in the covariance matrix, the SVD finds optimal\n",
    "orthogonal transformations to align the components along the directions most\n",
    "strongly associated with these correlated relationships. Simultaneously,\n",
    "because orthogonal matrices have columns of unit-length, the SVD collects the\n",
    "absolute squared lengths of these components into the $\\mathbf{S}$ matrix.  In\n",
    "our example above in [Figure](#fig:pca_003), the two feature vectors were obviously correlated along the\n",
    "diagonal, meaning that PCA selected that diagonal direction as the principal\n",
    "component.\n",
    "\n",
    "[^covariance]: Note that these entries are constructed from the data\n",
    "using an estimator of the covariance matrix because we do not have\n",
    "the full probability densities at hand.\n",
    "\n",
    "We have seen that PCA is a powerful dimension reduction method that is\n",
    "invariant to linear transformations of the original feature space. However,\n",
    "this method performs poorly with transformations that are nonlinear. In that\n",
    "case, there are a wide range of extensions to PCA, such as Kernel PCA, that are\n",
    "available in Scikit-learn, which allow for embedding parameterized\n",
    "non-linearities into the PCA at the risk of overfitting.\n",
    "\n",
    "## Independent Component Analysis\n",
    "\n",
    "Independent Component Analysis (ICA) via the `FastICA` algorithm is also\n",
    "available in Scikit-learn. This method is fundamentally different from PCA\n",
    "in that it is the small differences between components that are emphasized,\n",
    "not the large principal components.  This method is adopted from signal\n",
    "processing.  Consider a matrix of signals ($\\mathbf{X}$) where the rows are\n",
    "the samples and the columns are the different signals. For example, these\n",
    "could be EKG signals from multiple leads on a single patient. The analysis\n",
    "starts with the following model,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"eq:ICA\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\mathbf{X} =  \\mathbf{S}\\mathbf{A}^T\n",
    "\\label{eq:ICA} \\tag{1}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " In other words, the observed signal matrix is an unknown mixture\n",
    "($\\mathbf{A}$) of some set of conformable, independent random sources\n",
    "$\\mathbf{S}$,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbf{S}=\\left[ \\mathbf{s}_1(t),\\mathbf{s}_2(t),\\ldots,\\mathbf{s}_n(t)\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The distribution on the random sources is otherwise unknown, except\n",
    "there can be at most one Gaussian source, otherwise, the mixing matrix\n",
    "$\\mathbf{A}$ cannot be identified because of technical reasons.  The problem in\n",
    "ICA is to find $\\mathbf{A}$ in Equation [1](#eq:ICA) and thereby un-mix the\n",
    "$s_i(t)$ signals, but this cannot be solved without a strategy to reduce the\n",
    "inherent arbitrariness in this formulation.  \n",
    "\n",
    "To make this concrete, let us simulate the situation with the following code,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(123456)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import matrix, c_, sin, cos, pi\n",
    "t = np.linspace(0,1,250)\n",
    "s1 = sin(2*pi*t*6)\n",
    "s2 =np.maximum(cos(2*pi*t*3),0.3)\n",
    "s2 = s2 - s2.mean()\n",
    "s3 = np.random.randn(len(t))*.1\n",
    "# normalize columns\n",
    "s1=s1/np.linalg.norm(s1)\n",
    "s2=s2/np.linalg.norm(s2)\n",
    "s3=s3/np.linalg.norm(s3)\n",
    "S =c_[s1,s2,s3] # stack as columns\n",
    "# mixing matrix\n",
    "A = matrix([[  1,  1,1],\n",
    "            [0.5, -1,3],\n",
    "            [0.1, -2,8]])\n",
    "X= S*A.T # do mixing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs=subplots(3,2,sharex=True)\n",
    "fig.set_size_inches((8,8))\n",
    "X = np.array(X)\n",
    "\n",
    "_=axs[0,1].plot(t,-X[:,0],'k-')\n",
    "_=axs[1,1].plot(t,-X[:,1],'k-')\n",
    "_=axs[2,1].plot(t,-X[:,2],'k-')\n",
    "_=axs[0,0].plot(t,s1,'k-')\n",
    "_=axs[1,0].plot(t,s2,'k-')\n",
    "_=axs[2,0].plot(t,s3,'k-')\n",
    "\n",
    "_=axs[2,0].set_xlabel('$t$',fontsize=18)\n",
    "_=axs[2,1].set_xlabel('$t$',fontsize=18)\n",
    "_=axs[0,0].set_ylabel('$s_1(t)$        ',fontsize=18,rotation='horizontal')\n",
    "_=axs[1,0].set_ylabel('$s_2(t)$        ',fontsize=18,rotation='horizontal')\n",
    "_=axs[2,0].set_ylabel('$s_3(t)$        ',fontsize=18,rotation='horizontal')\n",
    "for ax in axs.flatten():\n",
    "    _=ax.yaxis.set_ticklabels('')\n",
    "\n",
    "_=axs[0,1].set_ylabel('        $X_1(t)$',fontsize=18,rotation='horizontal')\n",
    "_=axs[1,1].set_ylabel('        $X_2(t)$',fontsize=18,rotation='horizontal')\n",
    "_=axs[2,1].set_ylabel('        $X_3(t)$',fontsize=18,rotation='horizontal')\n",
    "_=axs[0,1].yaxis.set_label_position(\"right\")\n",
    "_=axs[1,1].yaxis.set_label_position(\"right\")\n",
    "_=axs[2,1].yaxis.set_label_position(\"right\")\n",
    "\n",
    "fig.savefig('fig-machine_learning/pca_008.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/pca_008.png, width=500 frac=0.85] The left column shows the original signals and the right column shows the mixed signals. The object of ICA is to recover the left column from the right. <div id=\"fig:pca_008\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_008\"></div>\n",
    "\n",
    "<p>The left column shows the original signals and the right column shows the mixed signals. The object of ICA is to recover the left column from the right.</p>\n",
    "<img src=\"fig-machine_learning/pca_008.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    " The individual signals ($s_i(t)$) and their mixtures ($X_i(t)$) are\n",
    "shown in [Figure](#fig:pca_008). To recover the individual signals using ICA,\n",
    "we use the `FastICA` object and fit the parameters on the `X` matrix,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import FastICA\n",
    "ica = FastICA()\n",
    "# estimate unknown S matrix\n",
    "S_=ica.fit_transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The results of this estimation are shown in [Figure](#fig:pca_009),\n",
    "showing that ICA is able to recover the original signals from the observed\n",
    "mixture. Note that ICA is unable to distinguish the signs of the recovered\n",
    "signals or preserve the order of the input signals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs=subplots(3,2,sharex=True)\n",
    "fig.set_size_inches((8,8))\n",
    "X = np.array(X)\n",
    "\n",
    "_=axs[0,1].plot(t,-S_[:,2],'k-')\n",
    "_=axs[1,1].plot(t,-S_[:,1],'k-')\n",
    "_=axs[2,1].plot(t,-S_[:,0],'k-')\n",
    "_=axs[0,0].plot(t,s1,'k-')\n",
    "_=axs[1,0].plot(t,s2,'k-')\n",
    "_=axs[2,0].plot(t,s3,'k-')\n",
    "\n",
    "_=axs[2,0].set_xlabel('$t$',fontsize=18)\n",
    "_=axs[2,1].set_xlabel('$t$',fontsize=18)\n",
    "_=axs[0,0].set_ylabel('$s_1(t)$        ',fontsize=18,rotation='horizontal')\n",
    "_=axs[1,0].set_ylabel('$s_2(t)$        ',fontsize=18,rotation='horizontal')\n",
    "_=axs[2,0].set_ylabel('$s_3(t)$        ',fontsize=18,rotation='horizontal')\n",
    "for ax in axs.flatten():\n",
    "    _=ax.yaxis.set_ticklabels('')\n",
    "\n",
    "_=axs[0,1].set_ylabel('        $s_1^\\prime(t)$',fontsize=18,rotation='horizontal')\n",
    "_=axs[1,1].set_ylabel('        $s_2^\\prime(t)$',fontsize=18,rotation='horizontal')\n",
    "_=axs[2,1].set_ylabel('        $s_3^\\prime(t)$',fontsize=18,rotation='horizontal')\n",
    "_=axs[0,1].yaxis.set_label_position(\"right\")\n",
    "_=axs[1,1].yaxis.set_label_position(\"right\")\n",
    "_=axs[2,1].yaxis.set_label_position(\"right\")\n",
    "\n",
    "fig.savefig('fig-machine_learning/pca_009.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/pca_009.png, width=500 frac=0.85] The left column shows the original signals and the right column shows the signals that ICA was able to recover. They match exactly, outside of a possible sign change. <div id=\"fig:pca_009\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_009\"></div>\n",
    "\n",
    "<p>The left column shows the original signals and the right column shows the signals that ICA was able to recover. They match exactly, outside of a possible sign change.</p>\n",
    "<img src=\"fig-machine_learning/pca_009.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "To develop some intuition as to how ICA accomplishes this feat, consider the\n",
    "following two-dimensional situation with two uniformly distributed independent\n",
    "variables, $u_x,u_y \\sim \\mathcal{U}[0,1]$. Suppose we apply the\n",
    "following orthogonal rotation matrix to these variables,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{bmatrix}\n",
    "u_x^\\prime \\\\\\\n",
    "u_y^\\prime \n",
    "\\end{bmatrix}= \n",
    "\\begin{bmatrix}\n",
    "\\cos(\\phi) & -\\sin(\\phi) \\\\\\\n",
    "\\sin(\\phi) & \\cos(\\phi)\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "u_x \\\\\\\n",
    "u_y \n",
    "\\end{bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/pca_005.png, width=500 frac=0.85] The left panel shows two classes labeled on the $u_x,u_y$ uniformly independent random variables. The right panel shows these random variables after a rotation, which removes their mutual independence and makes it hard to separate the two classes along the coordinate directions. <div id=\"fig:pca_005\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_005\"></div>\n",
    "\n",
    "<p>The left panel shows two classes labeled on the $u_x,u_y$ uniformly independent random variables. The right panel shows these random variables after a rotation, which removes their mutual independence and makes it hard to separate the two classes along the coordinate directions.</p>\n",
    "<img src=\"fig-machine_learning/pca_005.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    " The so-rotated variables $u_x^\\prime,u_y^\\prime$ are no longer\n",
    "independent, as shown in [Figure](#fig:pca_005). Thus, one way to think about\n",
    "ICA is as a search through orthogonal matrices so that the independence is\n",
    "restored. This is where the prohibition against Gaussian distributions arises.\n",
    "The two dimensional Gaussian distribution of independent variables is\n",
    "proportional the following,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "f(\\mathbf{x})\\propto\\exp(-\\frac{1}{2}\\mathbf{x}^T \\mathbf{x})\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Now, if we similarly rotated the $\\mathbf{x}$ vector as,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbf{y} = \\mathbf{Q} \\mathbf{x}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " the resulting density for $\\mathbf{y}$ is obtained by plugging in\n",
    "the following,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbf{x} = \\mathbf{Q}^T \\mathbf{y}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " because the inverse of an orthogonal matrix is its transpose, we obtain"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "f(\\mathbf{y})\\propto\\exp(-\\frac{1}{2}\\mathbf{y}^T \\mathbf{Q}\\mathbf{Q}^T \\mathbf{y})=\\exp(-\\frac{1}{2}\\mathbf{y}^T \\mathbf{y})\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " In other words, the transformation is lost on the $\\mathbf{y}$\n",
    " variable. This means that ICA cannot search over orthogonal transformations if\n",
    " it is blind to them, which explains the restriction of Gaussian random\n",
    " variables. Thus, ICA is a method that seeks to maximize the non-Gaussian-ness\n",
    " of the transformed random variables.  There are many methods to doing this,\n",
    " some of which involve cumulants and others that use the\n",
    "*negentropy*,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathcal{J}(Y) = \\mathcal{H}(Z)-\\mathcal{H}(Y)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " where $\\mathcal{H}(Z)$ is the information entropy of the\n",
    "Gaussian random variable $Z$ that has the same variance as $Y$. Further\n",
    "details would take us beyond our scope, but that is the outline of how\n",
    "the FastICA algorithm works.\n",
    "\n",
    "The implementation of this method in Scikit-learn includes two different ways\n",
    "of extracting more than one independent source component. The *deflation*\n",
    "method iteratively extracts one component at a time using a incremental\n",
    "normalization step. The *parallel* method also uses the single-component method\n",
    "but carries out normalization of all the components simultaneously, instead of\n",
    "for just the newly computed component.  Because ICA extracts\n",
    "independent components, a whitening step is used beforehand to balance the\n",
    "correlated components from the data matrix. Whereas PCA returns\n",
    "uncorrelated components along dimensions optimal for Gaussian random\n",
    "variables, ICA returns components that are as far from the Gaussian density\n",
    "as possible.\n",
    "\n",
    "The left panel on [Figure](#fig:pca_005) shows the orignal uniform random\n",
    "sources. The white and black colors distinguish between two classes. The right\n",
    "panel shows the mixture of these sources, which is what we observe as input\n",
    "features. The top row of [Figure](#fig:pca_006) shows the PCA (left) and ICA\n",
    "(right) transformed data spaces.  Notice that ICA is able to un-mix the two\n",
    "random sources whereas PCA transforms along the dominant diagonal. Because ICA\n",
    "is able to preserve the class membership, the data space can be reduced to two\n",
    "non-overlapping sections, as shown. However, PCA cannot achieve a similiar\n",
    "separation because the classes are mixed along the dominant diagonal that PCA\n",
    "favors as the main component in the decomposition. \n",
    "\n",
    "<!-- dom:FIGURE: [fig-machine_learning/pca_006.png, width=500 frac=0.85]  The panel on the top left shows two classes in a plane after a  rotation. The bottom left panel shows the result of dimensionality reduction using PCA, which causes mixing between the two classes. The top right panel shows the ICA transformed output and the lower right panel shows that, because ICA was able to un-rotate the data, the lower dimensional data maintains the separation between the classes. <div id=\"fig:pca_006\"></div>  -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:pca_006\"></div>\n",
    "\n",
    "<p>The panel on the top left shows two classes in a plane after a  rotation. The bottom left panel shows the result of dimensionality reduction using PCA, which causes mixing between the two classes. The top right panel shows the ICA transformed output and the lower right panel shows that, because ICA was able to un-rotate the data, the lower dimensional data maintains the separation between the classes.</p>\n",
    "<img src=\"fig-machine_learning/pca_006.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "For a good principal component analysis treatment, see  [[richert2013building]](#richert2013building),\n",
    "[[alpaydin2014introduction]](#alpaydin2014introduction), [[cuesta2013practical]](#cuesta2013practical), and\n",
    "[[izenman2008modern]](#izenman2008modern). Independent Component Analysis is discussed in more detail\n",
    "in [[hyvarinen2004independent]](#hyvarinen2004independent).\n",
    "\n",
    "<!-- #  *Learning from Data*, p. 263 -->\n",
    "<!-- #  *Building machine learning systems*, p.231 -->\n",
    "<!-- #  *Introduction to machine learning by Alpaydin*, p148 -->\n",
    "<!-- #  *Practical Data Analysis Cuesta*,p.143 -->\n",
    "<!-- #  *Modern Multivariate statistical techniques Izenman*, p.553, 558 -->\n",
    "<!-- #  *Independent Component Analysis Hyvarinen.pdf*, p.147 -->"
   ]
  }
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